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Conventional acceleration records do not properly account for the observed coseismic ground displacements, thus leading to an inaccurate definition of the seismic demand needed for the design of flexible (long period) structures. Large coseismic displacements observed during the 27 February 2010 Maule earthquake suggest that this effect should be included in the design of flexible structures by modifying the design ground motions and spectra considered. Consequently, Green's functions are used herein to compute synthetic low-frequency seismograms that are consistent with the coseismic displacement field obtained from interferometry using synthetic aperture radar (SAR) images. In this case, the coseismic displacement field was determined by interfering twenty SAR images of the Advanced Land Observation Satellite (ALOS)/PALSAR satellite taken between 12 October 2007 and 28 May 2010. These images cover the region affected by the 2010 M-w 8.8 Maule earthquake. Synthetic broadband seismograms are built by superimposing the low-pass filtered synthetic low-frequency seismograms with high-frequency strong-motion data. The broadband seismograms generated are then consistent with the coseismic displacement field and the high-frequency content of the earthquake. A sensitivity analysis is performed using three different fault and slip parameters, the rupture velocity, the corner frequency, and the slip rise time. Results show that the optimal corner frequency of the low-pass filter f(c) = 1/T-c, leads to a trade-off between acceleration and displacement accuracy. Furthermore, spectral response for long periods, say T >= 8 s, is relatively insensitive to the value of T-c, whereas shorter periods are strongly dependent on both the slip rise time and T-c. In general, larger displacements consistent with coseismic data are obtained using this technique instead of digitally processing the acceleration ground-motion records.

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... It has been shown for instance, that different values of slip rise-time have an important influence on the frequency content of the synthetic displacements produced (e.g. Fortuño et al. 2014). Consequently, the general aim of this work is to provide information to better characterize synthetic seismic scenarios for structural design purposes. ...

... Together they represent 8 different physically plausible seismic scenarios used to estimate low-frequency synthetic ground motions using the process described elsewhere (e.g. Fortuño et al. 2014). Spectral displacement and velocity responses are computed at four control sites and a sensitivity approach is used to estimate the expected value and variance of the spectral response values considering variations on average rupture velocity, slip rise-time, and foci location. ...

... Low-frequency synthetic ground motions were generated for each seismic scenario using the discrete wavenumber method (Zhu and Rivera 2002), which computes the Green's functions with a methodology similar to the one described elsewhere (e.g. Aki and Richards 2009;Fortuño et al. 2014). For a given scenario, the dynamic response at a specific site is computed considering the contribution of the slip on all elements (sub-faults) within the fault surface. ...

This research performs a sensitivity analysis of response spectrum values for various physical earthquake parameters, which are used to generate synthetic seismograms consistent with the expected seismicity in north Chile. Sensitivity analyses are based on the earthquake scenario and slip distribution model of the 2014, Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 8.1 Pisagua earthquake, and seven other physically plausible interplate events for north Chile. A finite-fault rupture model, and slip distribution of the Pisagua earthquake, were obtained using inversion of InSAR and GPS data. Three other rupture models based on previous studies of interplate locking for north Chile and capable of generating Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 8.3–8.6 earthquakes with an estimated maximum slip of 9.2 m, were incorporated in the analyses. Also, four additional scenarios with moment magnitudes in the range Mw\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_w$$\end{document} 8.6–8.9 were generated by concatenating these physical scenarios into larger rupture areas within the north segment. Using these scenarios, synthetic ground motions were built at four observation sites: Pisagua, Iquique, Tocopilla, and Calama. Response sensitivity was studied for three key rupture parameters: mean rupture velocity, slip rise-time, and rupture directivity. Responses selected were peak ground displacement (PGD), spectral pseudo-velocities, Sv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_v$$\end{document}, and spectral displacements, Sd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_d$$\end{document}. First and second order variations of PGD, Sv\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_v$$\end{document}, and Sd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_d$$\end{document} relative to the source parameters were computed and used together with a Taylor series expansion to propagate uncertainty into the responses as a function of vr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_r$$\end{document} and rise-time tr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_r$$\end{document}. To study the effect of rupture directivity, three different foci locations were considered for each scenario: north, south, and at the centroid of the slip model. Response PGD values show no clear trends with rupture velocity, vr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_r$$\end{document}; however, the variability increases as the system period increases. The effect of the slip rise-time is significant, and as tr\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t_r$$\end{document} increases, the spectral responses tend to decrease, suggesting that shorter slip rise-times lead to higher seismic demands in long period structures. The results obtained for the directivity analysis suggest that two factors control the expected waveforms and spectral responses: first, the direction of the rupture relative to the location of each site, and the hypocentral distance.

... Thus, we do not aim to recover real displacements in this work and provide displacements traces for referential use only. Some works were able to match the observed residual InSAR displacements (e.g., Abell et al., 2011;Fortuño et al., 2014), but this is not feasible for an entire database at the moment. ...

Since the 1985 M 8.0 central Chile earthquake, national strong-motion seismic networks have recorded ten megathrust earthquakes with magnitudes greater than M 7.5 at the convergent margin, defined by the contact between the Nazca and South American plates. The analysis of these earthquake records have led to improved hazard analyses and design codes for conventional and seismically protected structures. Although strong-motion baseline correction is required for a meaningful interpretation of these records, correction methods have not been applied consistently in time. The inconsistencies between correction methods have been neglected in the practical use of these records in practice. Consequently, this work aims to provide a new strong-motion database for researchers and engineers, which has been processed by traceable and consistent data processing techniques. The record database comes from three uncorrected strong motion Chilean databases. All the records are corrected using a four-step novel methodology, which detects the P-wave arrival and introduces a baseline correction based on the reversible-jump Markov chain Monte Carlo method. The resulting strong motion database has more than 2000 events from 1985 to the date, and it is available to download at the Simulation Based Earthquake Risk and Resilience of Interdependent Systems and Networks (SIBER-RISK) project website.

... Lay et al. (2012) and Palo et al. (2014), among others, used back-projection imaging with teleseismic shortperiod waveforms to delineate the area of the megathrust where high-frequency seismic energy was radiated Figure 1a. (a) Coseismic slip in the deeper part of the megathrust from the eight models used to derive the average in Figure 1a (solid lines) and four other models (dashed lines) (Fortuño et al., 2014;Hayes et al., 2013;Lin et al., 2013;Lorito et al., 2011). Inset shows the entire profile and the portion displayed in this figure (lower right box). ...

What controls subduction megathrust seismogenesis downdip of the mantle wedge corner (MWC)? We propose that, in the region of the 2010 Mw=8.8 Maule, Chile, earthquake, serpentine minerals derived from the base of the hydrated mantle wedge exert a dominant control. Based on modeling, we predict that the megathrust fault zone near the MWC contains abundant lizardite/chrysotile‐rich serpentinite that transforms to antigorite‐rich serpentinite at greater depths. From the MWC at 32–40 km depth to at least 55 km, the predominantly velocity‐strengthening megathrust accommodated dynamic propagation of the 2010 rupture but with small slip and negative stress drop. The downdip distribution of interplate aftershocks exhibits a gap around the MWC that can be explained by the velocity‐strengthening behavior of lizardite/chrysotile. Interspersed velocity‐weakening and dynamic weakening antigorite‐rich patches farther downdip may be responsible for increased abundance of aftershocks and possibly for some of the high‐frequency energy radiation during the 2010 rupture.

... . These include solutions to inversions based purely on teleseismic waveform data [e.g.Hayes, 2010a, b;Shao et al., 2010;Sladen, 2010;Pulido et al., 2011;Hayes et al., 2013;Benavente and Cummins, 2013]; geodetic data [e.g.Tong et al., 2010;Luttrell et al., 2011;Pollitz et al., 2011;Moreno et al., 2012;Fortuño et al., 2014]; and joint inversions combining geodetic with other data types [e.g.Delouis et al., 2010; Sladen and Owen, 2010; Vigny et al., 2011; Lorito et al., 2011; Fujii and Satake, 2013; Lin et al., 2013; Yue et al., 2014]. It is noted that some of these models correspond to the latest parameterizations of previously published results. ...

The variability in obtaining estimates of tsunami inundation and runup on a near-real-time tsunami hazard assessment setting is evaluated. To this end, 19 different source models of the Maule Earthquake were considered as if they represented the best available knowledge an early tsunami warning system could consider. Results show that large variability can be observed in both coseismic deformation and tsunami variables such as inundated area and maximum runup. This suggests that using single source model solutions might not be appropriate unless categorical thresholds are used. Nevertheless, the tsunami forecast obtained from aggregating all source models is in good agreement with observed quantities, suggesting that the development of seismic source inversion techniques in a Bayesian framework or generating stochastic finite fault models from a reference inversion solution could be a viable way of dealing with epistemic uncertainties in the framework of nearly-real-time tsunami hazard mapping.

... It is concluded, however, that such approach may underestimate local amplification effects in soft soil sites, or at very short rupture distances. In these cases, more detailed techniques for the generation of synthetic ground motions, like stochastic (e.g., Motazedian and Atkinson 2005), hybrid (e.g., Fortuno et al. 2014) or physics-based models (e.g., Papageorgiou and Aki 1983a, b), could be used to capture in finer detail the effects of local amplification, directivity, and different slip distributions. On the other hand, calibration of GMPEs or strong motion simulation techniques is generally hindered by the scarcity of seismic records and accurate V S30 measurements and reliable site classification data for the recording stations. ...

Risk evaluation and loss analysis is key in foreseeing the impact of disasters caused by natural hazards and may contribute effectively in improving resilience in a community through the pre-evaluation of preparedness and mitigation actions. The pilot study presented herein is for the Chilean city of Iquique, which is located at the core of a seismic gap that extends from south Perú to north Chile, and has strategic geopolitical and economic importance for the country. The region was hit April 1, 2014, by an \(M_\mathrm{w}\) 8.2 earthquake that caused only moderate damage, but seismological evidence suggests that there is still a potential for a much larger event in the region. Therefore, a careful damage assessment study is fundamental to anticipate the possible physical, social, and economic consequences that Iquique may face in the future. In this work, the HAZUS-MH platform was adapted and used to simulate a set of ten plausible physics-based future seismic scenarios with magnitudes ranging from \(M_\mathrm{w}\) 8.40 to \(M_\mathrm{w}\) 8.98, which were proposed based on an analysis of interplate locking and the residual slip potential remaining after the April 1, 2014, earthquake. Successful application of this damage assessment methodology relies on the construction of a comprehensive exposure model that takes into account regional features and a good characterization of the physical vulnerabilities. For Iquique, a large body of public and local data was used to develop a detailed inventory of physical and social assets including an aggregated building count, demographics, and essential facilities. To characterize the response of the built environment to seismic demand, appropriate HAZUS fragility curves were applied, and outcomes were validated against the damage observed in the 2014 earthquake. After satisfactory testing, a deterministic earthquake damage assessment study was carried out for the collection of predictive scenarios aimed to estimate their expected impacts. This analysis provides data for future evaluations of different physical and social mitigation measures for the city.

... Delouis et al. 2010;Lin et al. 2013;Tong et al. 2010;Vigny et al. 2011) have obtained models of co-seismic slip distributions for the 2010 Maule earthquake using InSAR and GPS data. Shown in Figure 1 is the interferogram done after the earthquake (Fortuño et al. 2014), which shows the extension of the fault, as well as the distribution of slip obtained through inversion of ascending interferometric images. Slip models differ among authors, but all show that the slip direction is predominantly updip with a downdip rupture limit that ends at the intersection of the subduction plate with the continental Moho (Tong et al. 2010). ...

At 3:34AM local time, on February 27 th , 2010, a moment magnitude Mw 8.8 megathrust earthquake struck offshore the coast of Chile. The earthquake ruptured a 540 by 200 km mature seismic gap of the underlying subduction pacific plate interlocking mechanism. More than 75% of the 16 million Chileans spread over several large urban areas in the center-south of the country were affected by the earthquake, which caused 521 fatalities with 124 of them due to the tsunami, and an overall damage estimate of USD 30 billion. Because the earthquake struck the most densely populated area of the country, it represents a very unique opportunity to reflect on its ubiquitous impact over many different physical and social systems. The reflection contained in this article occurs five years later, once reconstruction and recovery are complete from this longitudinal wound of the country. Seismic codes have changed, research on the supposedly indestructible reinforced concrete shear walls has been done, new seismic protection technologies have been incorporated, and whole new seismic standards have been adopted by communities and people. The price it took was quite high, but we can confidently say that Chile is better prepared today for the next large earthquake.

... The magnitude 8.8 Maule earthquake on February 27th, 2010, the largest earthquake ever recorded instrumentally in Chile, ruptured about 500 km by 140 km of the central-south region of Chile (Ruiz et al. 2012;Fortuño et al. 2014). A large tsunami was also triggered as a result of the earthquake, which inundated and devastated several towns along the coast of central Chile. ...

About 2 % of reinforced concrete (RC) buildings taller than nine stories suffered important structural damage during 2010 Chile earthquake. The typical structural configuration of residential buildings is characterized by a large number of RC structural walls which provides high lateral stiffness and strength. The first objective of this paper is to obtain global geometric and design parameters of RC structural walls in damaged buildings and correlate their values with the observed damage. The second objective is to compare the roof displacement capacity with the roof displacement demand in critical walls, and hence, try to explain the observed damage. The wall parameters were obtained from five representative damaged structural wall buildings; these are: wall thickness, aspect ratio, axial load, reinforcement ratios, and the ratio between horizontal reinforcement spacing and the vertical bar diameter. The roof displacement capacity is obtained using a plastic hinge approach, and the ACI 318-08 approach, since both methods are proposed in the current Chilean seismic code. The displacement demand is estimated from ground motions recorded in the vicinity of the buildings. It is found that values of wall parameters correlate well with the observed damage. The structural walls were subjected to relatively high axial loads, and some walls included a large amount of vertical reinforcement to provide the required strength, but had inadequate transverse reinforcement thus compromising ductility. Findings from this research suggest that the plastic hinge approach is inadequate to estimate the roof displacement capacity and lacks correlation with the observed damage. Moreover, the use of the ACI 318-08 approach to estimate the roof displacement capacity is also inadequate, but leads to better predictions of wall displacement capacity. As shown by the results of response history analysis, the failure of walls was triggered by high axial loads rather than flexural deformation.

Nonlinear dynamic analysis techniques have made significant progress in the last 20 years, providing powerful tools for assessing structural damage and potential building collapse mechanisms. The fact that several reinforced concrete shear wall residential buildings underwent severe structural damage in walls at the lower building levels during the 2010 Maule earthquake (Chile) presents a scientific opportunity to assess the predictive quality of these techniques. The objective of this research is to compare building responses using two completely different three-dimensional nonlinear dynamic models and study in detail the observed damage pattern and wall collapse of one reinforced concrete shear wall building in Santiago, Chile. The first model is a mixed fiber-shell model developed in MATLAB, and the second is a shell finite element model developed in the software DIANA. Results of both models are consistent with the hypothesis that high axial loads trigger a limited ductility failure in critical walls at roof-to-base drift ratios less than 0.34% with little capacity of hysteretic energy dissipation, which contradicts the ductile design philosophy of current code provisions.

An inverse method to find optimum fault parameters from geodetic data with random errors is extended so as to be applicable to a case of the data including a systematic error caused by movements of reference points in triangulation. Application of the new inverse method to static displacement data associated with the Kanto earthquake of 1923 yields a dislocation source model which adequately explains both the seismological and the geodetic data.
From the geodetic data, it is found that the fault motion of the Kanto earthquake is a reverse, right-lateral slip of 4.8m with a slip-angle of 140° on a plane which dips 25° towards N24°E, where the slip-angle is measured counterclockwise from a strike on the fault plane. The fault length, width, and the depth to the upper fault margin are determined as 95km, 54km, and 1.5km respectively. The seismic moment and stress drop of this earthquake are estimated to be 8.4×10²⁷ dyne·cm and 45 bars, respectively.
Taking the static fault solution as the basic model, the dynamic process of the fracture is investigated on the basis of the long-period seismograms recorded at Hongo, Tokyo. The result shows that the rupture starts from a relocated hypocenter, 35.41°N, 139.22°E and 13.5km (depth), and extends outwards on the fault plane with a propagating velocity of the rupture front of 2.0km/sec. The rise time of the source time function is assumed to be 5.0sec. The maximum amplitude of acceleration for a frequency range of 0.0-3.3Hz at Tokyo is estimated to be about 280gal for the horizontal component and to be 60gal for the vertical component, by applying an empirical formula to the calculated ground displacements.

Fling is the engineering term for the effects of the permanent tectonic offset, caused by a rupturing fault in the recorded ground motions near the fault. It is expressed by a one-sided pulse in ground velocity and a nonzero final displace-ment at the end of shaking. Standard processing of earthquake time histories removes some of the fling effects that may be required for engineering applications. A method to parameterize the fling-step time history and to superimpose it onto traditionally processed time histories has been developed by Abrahamson (2002). In this paper, we first present an update to the Abrahamson (2002) fling-step models, in which the fling step is parameterized as a single cycle of a sine wave. Parametric models are presented for the sine-wave amplitude (D site) and period (T f). The expressions for D site and T f are derived from an extensive set of finite-fault simulations conducted on the Southern California Earthquake Center broadband platform (see Data and Re-sources). The simulations were run with the Graves and Pitarka (2010) hybrid sim-ulation method and included strike-slip and reverse scenarios for magnitudes of 6.0– 8.2 and dips of 30 through 90. Next, an improved approach for developing design ground motions with fling effects is presented, which deals with the problem of double-counting intermediate period components that were not removed by the stan-dard ground-motion processing. Finally, the results are validated against a set of 84 empirical recordings containing fling.

This paper describes refinements to the hybrid broadband ground-motion simulation methodology of Graves and Pitarka (2004), which combines a deterministic approach at low frequencies (f < 1 Hz) with a semistochastic approach at high frequencies (f > 1 Hz). In our approach, fault rupture is represented kinematically and incorporates spatial heterogeneity in slip, rupture speed, and rise time. The prescribed slip distribution is constrained to follow an inverse wavenumber-squared fall-off and the average rupture speed is set at 80% of the local shear-wave velocity, which is then adjusted such that the rupture propagates faster in regions of high slip and slower in regions of low slip. We use a Kostrov-like slip-rate function having a rise time proportional to the square root of slip, with the average rise time across the entire fault constrained empirically. Recent observations from large surface rupturing earthquakes indicate a reduction of rupture propagation speed and lengthening of rise time in the near surface, which we model by applying a 70% reduction of the rupture speed and increasing the rise time by a factor of 2 in a zone extending from the surface to a depth of 5 km. We demonstrate the fidelity of the technique by modeling the strong-motion recordings from the Imperial Valley, Loma Prieta, Landers, and Northridge earthquakes.

The 27 February 2010 Chile (Mw 8.8) earthquake is the fifth largest earthquake to strike during the age of seismological instrumentation. The faulting geometry, slip distribution, seismic moment, and moment-rate function are estimated from broadband teleseismic P, SH, and Rayleigh wave signals. We explore some of the trade-offs in the rupture-process estimation due to model parameterizations, limited teleseismic sampling of seismic phase velocities, and uncertainty in fault geometry. The average slip over the ∼81,500 km2 rupture area is about 5 m, with slip concentrations down-dip, up-dip and southwest, and up-dip and north of the hypocenter. Relatively little slip occurred up-dip/offshore of the hypocenter. The average rupture velocity is ∼2.0–2.5 km/s.

We use a combination of satellite radar and GPS data to estimate the slip distribution of the 1999 Mw 7.1 Hector Mine Earthquake, a right-lateral strikeslip earthquake that occurred on a northwest–southeast striking fault in
the southern California Mojave Desert. The data include synthetic aperture radar interferograms (InSAR) from both ascending
and descending orbits, radar amplitude image offset fields (SARIO) for both ascending and descending azimuth directions, and
campaign GPS observations from 55 stations provided by Agnew et al. (2002). We model the fault with nine segments derived from the field-mapped fault rupture, the SARIO data, and aftershock locations.
We first estimate the dip of each fault segment, as well as a single constant strike-slip component across each segment, resulting
in an average dip of 83° to the northeast and slip of up to 5.6 m. Then, we fix the optimal fault segment dip, discretize
the fault segments into 1.5 km × 1.5 km patches, and solve for the variable slip distribution using a nonnegative least-squares
method that includes an appropriate degree of smoothing. Our preferred solution has both right-lateral strike-slip and reverse
faulting. The estimated geodetic moment is 5.93 × 1019 N m (Mw 7.1), similar to seismological estimates, indicating that there are insignificant interseismic and postseismic deformation
signals in the data. We find strike-slip displacements of up to 6.0 m and reverse faulting of up to 1.6 m, with the maximum
slip located just northwest of the epicenter. Most of the slip is concentrated northwest and south of the epicenter; little
slip is found on the northeastern branch of the fault. The SARIO data and our modeling indicate that the amount and extent
of surface fault rupture were underestimated in the field.

We present a new procedure for the determination of rupture complexity from a joint inversion of static and seismic data. Our fault parameterization involves multiple fault segments, variable local slip, rake angle, rise time, and rupture velocity. To separate the spatial and temporal slip history, we introduce a wavelet transform that proves effective at studying the time and frequency characteristics of the seismic waveforms. Both data and synthetic seismograms are transformed into wavelets, which are then separated into several groups based on their frequency content. For each group, we use error functions to compare the wavelet amplitude variation with time between data and synthetic seismograms. The function can be an L1 L2 norm or a correlative function based on the amplitude and scale of wavelet functions. The objective function is defined as the weighted sum of these functions. Subsequently, we developed a finite-fault inversion routine in the wavelet domain. A simulated annealing algorithm is used to determine the finite-fault model that minimizes the objective function described in terms of wavelet coefficients. With this approach, we can simultaneously invert for the slip amplitude, slip direction, rise time, and rupture velocity efficiently. Extensive experiments conducted on synthetic data are used to assess the ability to recover rupture slip details. We, also explore slip-model stability for different choices of layered Earth models assuming the geometry encountered in the 1999 Hector Mine, California, earthquake.

The Concepción–Constitución area [35–37°S] in South Central Chile is very likely a mature seismic gap, since no large subduction earthquake has occurred there since 1835. Three campaigns of global positioning system (GPS) measurements were carried out in this area in 1996, 1999 and 2002. We observed a network of about 40 sites, including two east–west transects ranging from the coastal area to the Argentina border and one north–south profile along the coast. Our measurements are consistent with the Nazca/South America relative angular velocity (55.9°N, 95.2°W, 0.610°/Ma) discussed by Vigny et al. (2008, this issue) which predicts a convergence of 68mm/year oriented 79°N at the Chilean trench near 36°S. With respect to stable South America, horizontal velocities decrease from 45mm/year on the coast to 10mm/year in the Cordillera. Vertical velocities exhibit a coherent pattern with negative values of about 10mm/year on the coast and slightly positive or near zero in the Central Valley or the Cordillera. Horizontal velocities have formal uncertainties in the range of 1–3mm/year and vertical velocities around 3–6mm/year. Surface deformation in this area of South Central Chile is consistent with a fully coupled elastic loading on the subduction interface at depth. The best fit to our data is obtained with a dip of 16±3°, a locking depth of 55±5km and a dislocation corresponding to 67mm/year oriented 78°N. However in the northern area of our network the fit is improved locally by using a lower dip around 13°. Finally a convergence motion of about 68mm/year represents more than 10m of displacement accumulated since the last big interplate subduction event in this area over 170 years ago (1835 earthquake described by Darwin). Therefore, in a worst case scenario, the area already has a potential for an earthquake of magnitude as large as 8–8.5, should it happen in the near future.

Tectonic deformation from the 2010 Maule (Chile) Mw 8.8 earthquake included both uplift and subsidence along about 470 km of the central Chilean coast. In the south, deformation included as much as 3 m of uplift of the Arauco Peninsula, which produced emergent marine platforms and affected harbor infrastructure. In the central part of the deformation zone, north of Constitución, coastal subsidence drowned supratidal floodplains and caused extensive shoreline modification. In the north, coastal areas experienced either slight uplift or no detected change in land level. Also, river-channel deposition and decreased gradients suggest tectonic subsidencemay have occurred in inland areas. The overall north-south pattern of 2010 coastal uplift and subsidence is similar to the average crestal elevation of the Coast Range between latitudes 33°S and 40°S. This similarity implies that the topography of the Coast Range may reflect long-term permanent strain accrued incrementally over many earthquake cycles.

Geophysical applications of radar inter-ferometry to measure changes in the Earth's surface have exploded in the early 1990s. This new geodetic technique calculates the interference pattern caused by the difference in phase between two images acquired by a spaceborne synthetic aperture radar at two distinct times. The resulting interferogram is a contour map of the change in distance between the ground and the radar instrument. These maps provide an unsurpassed spatial sampling density (100 pixels km 2), a competitive pre-cision (1 cm), and a useful observation cadence (1 pass month 1). They record movements in the crust, pertur-bations in the atmosphere, dielectric modifications in the soil, and relief in the topography. They are also sensitive to technical effects, such as relative variations in the radar's trajectory or variations in its frequency standard. We describe how all these phenomena contribute to an interferogram. Then a practical summary explains the techniques for calculating and manipulating interfero-grams from various radar instruments, including the four satellites currently in orbit: ERS-1, ERS-2, JERS-1, and RADARSAT. The next chapter suggests some guide-lines for interpreting an interferogram as a geophysical measurement: respecting the limits of the technique, assessing its uncertainty, recognizing artifacts, and dis-criminating different types of signal. We then review the geophysical applications published to date, most of which study deformation related to earthquakes, volca-noes, and glaciers using ERS-1 data. We also show examples of monitoring natural hazards and environ-mental alterations related to landslides, subsidence, and agriculture. In addition, we consider subtler geophysical signals such as postseismic relaxation, tidal loading of coastal areas, and interseismic strain accumulation. We conclude with our perspectives on the future of radar interferometry. The objective of the review is for the reader to develop the physical understanding necessary to calculate an interferogram and the geophysical intu-ition necessary to interpret it.

Large earthquakes produce crustal deformation that can be quantified by geodetic measurements, allowing for the determination of the slip distribution on the fault. We used data from Global Positioning System (GPS) networks in Central Chile to infer the static deformation and the kinematics of the 2010 moment magnitude (M(w)) 8.8 Maule megathrust earthquake. From elastic modeling, we found a total rupture length of ~500 kilometers where slip (up to 15 meters) concentrated on two main asperities situated on both sides of the epicenter. We found that rupture reached shallow depths, probably extending up to the trench. Resolvable afterslip occurred in regions of low coseismic slip. The low-frequency hypocenter is relocated 40 kilometers southwest of initial estimates. Rupture propagated bilaterally at about 3.1 kilometers per second, with possible but not fully resolved velocity variations.

Radar interferometry from the ALOS satellite captured the coseismic ground deformation associated with the 2010 Mw 8.8 Maule, Chile earthquake. The ALOS interferograms reveal a sharp transition in fringe pattern at ~150 km from the trench axis that is diagnostic of the downdip rupture limit of the Maule earthquake. An elastic dislocation model based on ascending and descending ALOS interferograms and 13 near-field 3-component GPS measurements reveals that the coseismic slip decreases more or less linearly from a maximum of 17 m (along-strike average of 6.5 m) at 18 km depth to near zero at 43–48 km depth, quantitatively indicating the downdip limit of the seismogenic zone. The depth at which slip drops to near zero appears to be at the intersection of the subducting plate with the continental Moho. Our model also suggests that the depth where coseismic slip vanishes is nearly uniform along the strike direction for a rupture length of ~600 km. The average coseismic slip vector and the interseismic velocity vector are not parallel, which can be interpreted as a deficit in strike-slip moment release.

We use interferometric synthetic aperture radar, GPS, and teleseismic data to constrain the relative location of coseismic slip from 11 earthquakes on the subduction interface in northern Chile (23°–25°S) between the years 1993 and 2000. We invert body wave waveforms and geodetic data both jointly and separately for the four largest earthquakes during this time period (1993 M_w 6.8; 1995 M_w 8.1; 1996 M_w 6.7; 1998 M_w 7.1). While the location of slip in the teleseismic-only, geodetic-only, and joint slip inversions is similar for the small earthquakes, there are differences for the 1995 M_w 8.1 event, probably related to nonuniqueness of models that fit the teleseismic data. There is a consistent mislocation of the Harvard centroid moment tensor locations of many of the 6 < M_w < 8 earthquakes by 30–50 km toward the trench. For all models, the teleseismic data are better able to resolve fine details of the earthquake slip distribution. The 1995 earthquake did not rupture to the maximum depth of the seismogenic zone (as defined by the other earthquakes). In addition to the above events, we use only teleseismic data to determine the rupture characteristics of four other M_w > 6 earthquakes, as well as three M_w > 7 events from the 1980s. All of these earthquakes appear to rupture different portions of the fault interface and do not rerupture a limited number of asperities.

We use seismic and geodetic data both jointly and separately to constrain coseismic slip from the 12 November 1996 M_w 7.7 and 23 June 2001 M_w 8.5 southern Peru subduction zone earthquakes, as well as two large aftershocks following the 2001 earthquake on 26 June and 7 July 2001. We use all available data in our inversions: GPS, interferometric synthetic aperture radar (InSAR) from the ERS-1, ERS-2, JERS, and RADARSAT-1 satellites, and seismic data from teleseismic and strong motion stations. Our two-dimensional slip models derived from only teleseismic body waves from South American subduction zone earthquakes with M_w > 7.5 do not reliably predict available geodetic data. In particular, we find significant differences in the distribution of slip for the 2001 earthquake from models that use only seismic (teleseismic and two strong motion stations) or geodetic (InSAR and GPS) data. The differences might be related to postseismic deformation or, more likely, the different sensitivities of the teleseismic and geodetic data to coseismic rupture properties. The earthquakes studied here follow the pattern of earthquake directivity along the coast of western South America, north of 5°S, earthquakes rupture to the north; south of about 12°S, directivity is southerly; and in between, earthquakes are bilateral. The predicted deformation at the Arequipa GPS station from the seismic-only slip model for the 7 July 2001 aftershock is not consistent with significant preseismic motion.

We observed vertically displaced coastal and river markers after the 27 February 2010 Chilean earthquake [moment magnitude (Mw) 8.8]. Land-level changes range between 2.5 and -1 meters, evident along an approximately 500-kilometers-long segment identified here as the maximum length of coseismic rupture. A hinge line located 120 kilometers from the trench separates uplifted areas, to the west, from subsided regions. A simple elastic dislocation model fits these observations well; model parameters give a similar seismic moment to seismological estimates and suggest that most of the plate convergence since the 1835 great earthquake was elastically stored and then released during this event.

Synthetic aperture radar interferometry is an imaging technique
for measuring the topography of a surface, its changes over time, and
other changes in the detailed characteristic of the surface. By
exploiting the phase of the coherent radar signal, interferometry has
transformed radar remote sensing from a largely interpretive science to
a quantitative tool, with applications in cartography, geodesy, land
cover characterization, and natural hazards. This paper reviews the
techniques of interferometry, systems and limitations, and applications
in a rapidly growing area of science and engineering

. We propose a new algorithm, a reflective Newton method, for the minimization of a quadratic function of many variables subject to upper and lower bounds on some of the variables. The method applies to a general (indefinite) quadratic function, for which a local minimizer subject to bounds is required, and is particularily suitable for the large-scale problem. Our new method exhibits strong convergence properties, global and quadratic convergence, and appears to have significant practical potential. Strictly feasible points are generated. Experimental results on moderately large and sparse problems support the claim of practicality for large-scale problems. 1 Research partially supported by the Applied Mathematical Sciences Research Program (KC04 -02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG0286ER25013. A000, and by the Computational Mathematics Program of the National Science Foundation under grant DMS-8706133, and by the Cornell Theory Cen...

A solution for the surface displacements due to buried dislocation sources in a multi-layered elastic medium is found using the Haskell (1964) paper as a starting point and more importantly, for notation. Through the introduction of some simple matrix operations, the Haskell (1964) solution is made simultaneously more compact and computationally stable. Time histories are computed for a perfectly elastic medium by performing classical contour integration in the complex wavenumber plane. A new aspect in the evaluation of those contours is introduced because of the recognition of nonzero singularity contributions of the Hankel and modified Bessel functions at k = 0. Theoretical ground motion time histories are presented to show the usefulness of the formulation. The overall objective of this paper is to incorporate the modifications made since 1964 to the Haskell (1964) paper in an easily understandable, step-by-step development.

The purpose of this study is to develop and test a procedure for simulating acceleration time histories of large subduction earthquakes. The ground motions of the large event are obtained by summing contributions from fault elements to simulate the propagation of rupture over the fault surface. The procedure has been tested against the recorded strong ground motions of the Mw = 8.0 Michoacan, Mexico, and Valparaiso, Chile, earthquakes of 1985. We find that models of heterogeneous slip in these events derived by other investigators from the analysis of teleseismic and near-source velocity seismograms also explain the shorter period motions of the recorded accelerograms. The procedure is applied in a companion paper to estimate strong ground motion characteristics in the Pacific Northwest region of the US from hypothesized Mw = 8 subduction earthquakes on the Cascadia plate interface. -from Authors

Using the fault slip determined by Sieh (1978a), the great 1857 California earthquake is modeled as a propagating fault buried in a realistic medium consisting of a two-layer crust overlying the mantle. The computation is carried out by the discrete wavenumber representation method (Bouchon, 1979). The resulting motion is almost purely horizontal throughout central and southern California, and, at most of the locations, the direction of severe ground shaking is oriented NE-SW. In the Los Angeles area, the peak displacement is about 30 cm, and the duration of severe ground motion is about 75 sec. Since our model does not include the effect of incoherent rupture propagation, our estimate should be considered as a lower bound. The simulated seismic motions are presented in the form of three-dimensional snapshots as well as in the usual form of time series at selected locations. The resultant near-field seismograms show a great diversity in the characteristic of motion as pointed out for actual near-field accelerograms by Hudson (1976). Our simulated motions appear to be in harmony with the description of the effect of the 1857 earthquake by contemporary accounts compiled by Agnew and Sieh (1978).

Residual displacements for large earthquakes can sometimes be determined from recordings on modern digital instruments, but baseline offsets of unknown origin make it difficult in many cases to do so. To recover the residual displacement, we suggest tailoring a correction scheme by studying the character of the velocity obtained by integration of zeroth-order-corrected acceleration and then seeing if the residual displacements are stable when the various parameters in the particular correction scheme are varied. For many seismological and engineering purposes, however, the residual displacements are of lesser importance than ground motions at periods less than about 20 sec. These ground motions are often recoverable with simple baseline correction and low-cut filtering. In this largely empirical study, we illustrate the consequences of various correction schemes, drawing primarily from digital recordings of the 1999 Hector Mine, California, earthquake. We show that with simple processing the displacement waveforms for this event are very similar for stations separated by as much as 20 km. We also show that a strong pulse on the transverse component was radiated from the Hector Mine earthquake and propagated with little distortion to distances exceeding 170 km; this pulse leads to large response spectral amplitudes around 10 sec.

We simulated broadband hard-rock ground-motion time histories for the Saint Louis, Missouri, metropolitan area due to three large earthquakes (6.5 =< Mw = 7.5), each occurring on the largest fault segment of the New Madrid fault zone at a distance of about 200 km. A deterministic procedure was implemented to simulate ground motion for frequencies less than 1 Hz for which the propagation effects were calculated using full-wave theory. For signals above 1 Hz, a semi-empirical simu-lation approach was used. The fault dimensions were defined in conformity with a constant stress-drop model developed for eastern North America; the fault width was constrained to a maximum depth of 16 km following the occurrence of the natural seismicity. For each event, we simulated broadband time histories for ten randomly generated slip models at eight sites distributed in various locations in the city of Saint Louis. This study shows that the level of peak ground motions at hard-rock sites in Saint Louis is small; the largest average peak horizontal ground-motion acceleration simulated is only 26.45 cm/sec 2 (1.96 cm/sec for the velocity) even for the largest event. To validate the simulation results, we examined regional accelerograms and their peak values and response spectra recorded during the 25 November 1988 Sag-uenay earthquake (Mw = 5.8) at distances further than 230 km from its epicenter to be consistent with the distance of the city of Saint Louis from the New Madrid earthquake zone. The Saguenay earthquake observations seem consistent with sim-ulation values obtained for the M w = 6.5 New Madrid earthquake. A preliminary equivalent linear analysis by applying these simulated motions at the base of a soil profile suggests that the level of ground motions is too weak to produce damaging effects in Saint Louis even for the largest event on the longest segment.

[1] Observations of coseismic and postseismic deformation associated with the 2010 Mw = 8.8 Maule earthquake in south-central Chile provide constraints on the spatial heterogeneities of frictional properties on a major subduction megathrust and how they have influenced the seismic rupture and postseismic effects. We find that the bulk of coseismic slip occurs within a single elongated patch approximately 460 km long and 100 km wide between the depths of 15 and 40 km. We infer three major patches of afterslip: one extends northward along strike and downdip of the major coseismic patch between 40 and 60 km depth; the other two bound the northern and southern ends of the coseismic patch. The southern patch offshore of the Arauco Peninsula is the only place showing resolvable afterslip shallower than 20 km depth. Estimated slip potency associated with postseismic slip in the 1.3 years following the earthquake amounts to 20–30% of that generated coseismically. Our estimates of the megathrust frictional properties show that the Arauco Peninsula area has positive but relatively low (a−b)σn values (0.01 ~ 0.22 MPa), that would have allowed dynamic rupture propagation into this rate-strengthening area and afterslip. Given the only modestly rate-strengthening megathrust friction in this region, the barrier effect may be attributed to its relatively large size of the rate-strengthening patch. Coseismic and postseismic uplift of the Arauco Peninsula exceeds interseismic subsidence since the time of the last major earthquake in 1835, suggesting that coseismic and postseismic deformation has resulted in some permanent strain in the forearc.

Strong-motion records from KiK-net and K-NET, along with 1 sample/s Global Positioning System (GPS) records from GEONET, were analyzed to determine the location, timing, and slip of subevents of the M 9 2011 Tohoku earthquake. Timing of arrivals on stations along the coast shows that the first subevent was located closer to the coast than subevent (2), which produced the largest slip. A waveform inversion of data from 0 to 0.2 Hz indicates that the first subevent primarily ruptured down-dip and north of the hypocenter and had an M of 8.5. The areas of this subevent that generated the low (<0.2 Hz) and high (>0.2 Hz) frequency energy are located in the same vicinity. The inversion result for the second subevent (M 9.0) has large slip on the shallow part of the fault with peak slip of about 65 m above about 25 km depth. This slip generated the tsunami. The preferred inversion has initiation of subevent 2 on the shallow portion of the fault so that rupture proceeded down-dip and mainly to the south. Subevent 2 started about 35 s after subevent 1, which allows for the possibility of dynamic triggering from subevent 1. The slip model predicts displacements comparable to those found from ocean-bottom transducers near the epicenter. At frequencies that most affect tall buildings (0.1-0.5 Hz), there is a strong pulse (subevent 3) in the strong-motion records that arrives after the near-field ramp from subevent 2. High-frequency subevent 3 was located down-dip and south of the high-slip portion of subevent 2 and was initiated as rupture from subevent 2 proceeded down-dip. The compact pulse for subevent 3 is modeled with an M 8.0 source in a 75 by 30 km area that ruptured down-dip and to the south with a high slip velocity, indicating high stress drop.

Interferometric Synthetic Aperture Radar (InSAR) observations are
sometimes the only geodetic data of large subduction-zone earthquakes.
However, these data usually suffer from spatially long-wavelength
orbital and atmospheric errors that can be difficult to distinguish from
the coseismic deformation and may therefore result in biased fault-slip
inversions. To study how well InSAR constrains fault-slip of large
subduction zone earthquakes, we use data of the 11 March 2011 Tohoku-Oki
earthquake (Mw 9.0) and test InSAR-derived fault-slip models
against models constrained by GPS data from the extensive nationwide
network in Japan. The coseismic deformation field was mapped using InSAR
data acquired from multiple ascending and descending passes of the ALOS
and Envisat satellites. We then estimated several fault-slip
distribution models that were constrained using the InSAR data alone,
onland and seafloor GPS/acoustic data, or combinations of the different
data sets. Based on comparisons of the slip models, we find that there
is no real gain by including InSAR observations for determining the
fault slip distribution of this earthquake. That said, however, some of
the main fault-slip patterns can be retrieved using the InSAR data alone
when estimating long wavelength orbital/atmospheric ramps as a part of
the modeling. Our final preferred fault-slip solution of the Tohoku-Oki
earthquake is based only on the GPS data and has maximum reverse- and
strike-slip of 36.0 m and 6.0 m, respectively, located northeast of the
epicenter at a depth of 6 km, and has a total geodetic moment is 3.6
× 1022 Nm (Mw 9.01), similar to
seismological estimates.

The Mw 8.8 Maule earthquake occurred off the coast of central
Chile on 2010 February 27 and was the sixth largest earthquake to be
recorded instrumentally. This subduction zone event was followed by
thousands of aftershocks both near the plate interface and in the
overriding continental crust. Here, we report on a pair of large shallow
crustal earthquakes that occurred on 2010 March 11 within 15 min of each
other near the town of Pichilemu, on the coast of the O'Higgins Region
of Chile. Field and aerial reconnaissance following the events revealed
no distinct surface rupture. We infer from geodetic data spanning both
events that the ruptures occurred on synthetic SW-dipping normal faults.
The first, larger rupture was followed by buried slip on a steeper fault
in the hangingwall. The fault locations and geometry of the two events
are additionally constrained by locations of aftershock seismicity based
on the International Maule Aftershock Data Set. The maximum slip on the
main fault is about 3 m and, consistent with field results, the onshore
slip is close to zero near the surface. Satellite radar data also reveal
that significant aseismic afterslip occurred following the two
earthquakes. Coulomb stress modelling indicates that the faults were
positively stressed by up to 40 bars as a result of slip on the
subduction interface in the preceding megathrust event; in other words,
the Pichilemu earthquakes should be considered aftershocks of the Maule
earthquake. The occurrence of these extensional events suggests that
regional interseismic compressive stresses are small. Several recent
large shallow crustal earthquakes in the overriding plate following the
2011 Mw 9.0 Tohoku-Oki earthquake in Japan may be an analogue
for the triggering process at Pichilemu.

Robust earthquake source parameters (e.g., location, seismic moment, fault geometry) are essential for reliable seismic hazard assessment and the investigation of large-scale tectonics. They are routinely estimated using a variety of data and techniques, such as seismic data and, more recently, Interferometric Synthetic Aperture Radar (InSAR). Comparisons between these two datasets are frequently made although not usually in a comprehensive way. This review compares source parameters from global and regional seismic catalogues with those from a recent database of InSAR parameters, which has been expanded with 18 additional source models for this study.

We estimated the possible range of long-period ground motion for sites located on a soft sedimentary basin in the immediate vicinity of a large earthquake. Since many large cities in the world (e.g., Los Angeles, San Francisco, and Tokyo) where many large structures have been recently constructed are located in this type of environment, a better understanding of long-period ground motion is becoming increasingly important. Our objective is to estimate the possible range of long-period ground motion, rather than ground motion for a specific fault model. We computed ground-motion time series and pseudo-velocity response spectra (PVS) for more than 5,000 models for the 1923 Kanto, Japan, earthquake (M w = 7.9) using 180 slip distributions, eight rupture geometry, and rupture velocities ranging from 1.5 to 3.0 krn/sec. Two seismograms recorded in Tokyo during the 1923 Kanto earthquake are used for comparison. The response spectra computed using seismologically reason- able sets of source parameters for the 1923 Kanto earthquake vary by more than an order of magnitude. At periods of 10 to 13 sec, they range from 25 to 170 cm/sec in Tokyo. For some combinations of model parameters, the response spectra exhibit peaks in the range of 10 to 13 sec. Many of the computed response spectra have peaks at periods longer than 10 sec, which is considerably longer than the dominant period (6 to 8 sec) estimated from studies of small earthquakes and microtremor measurements. Thus, the dominant period of the subsurface structure determined locally may not be representative of the dominant period of ground motion from a nearby large earthquake, which is controlled by rupture directivity and source depth. We performed a similar simulation for a hypothetical M w = 7.5 earthquake located beneath the Los Angeles basin. For a site just above the center of the fault, the ground-motion spectral amplitude at a period of 10 sec can vary from 50 to 350 cm/ sec. This range, though very large, is what is expected for a seismologically plausible range of source parameters.

We analyse radar interferometric and GPS observations of the displacement field from the 1995 July 30 Mw= 8.1 Antofagasta, Chile, earthquake and invert for the distribution of slip along the co-seismic fault plane. Using a fixed fault geometry, we compare the use of singular-value decomposition and constrained linear inversion to invert for the slip distribution and find that the latter approach is better resolved and more physically reasonable. Separate inversions using only GPS data, only InSAR data from descending orbits, and InSAR data from both ascending and descending orbits without the GPS data illustrate the complimentary nature of GPS and the presently available InSAR data. The GPS data resolve slip near GPS benchmarks well, while the InSAR provides greater spatial sampling. The combination of ascending and descending InSAR data contributes greatly to the ability of InSAR to resolve the slip model, thereby emphasizing the need to acquire this data for future earthquakes. The rake, distribution of slip and seismic moment of our preferred model are generally consistent with previous seismic and geodetic inversions, although significant differences do exist. GPS data projected in the radar line-of-sight (LOS) and corresponding InSAR pixels have a root mean square (rms) difference of about 3 cm. Comparison of our predictions of vertical displacement and observed uplift from corraline algae have an rms of 10 cm. Our inversion and previous results reveal that the location of slip might be influenced by the 1987 Mw= 7.5 event. Our analysis further reveals that the 1995 slip distribution was affected by a 1988 Mw= 7.2 event, and might have influenced a 1998 Mw= 7.0 earthquake that occurred downdip of the 1995 rupture. Our slip inversion reveals a potential change in mechanism in the southern portion of the rupture, consistent with seismic results. Predictions of the satellite LOS displacement from a seismic inversion and a joint seismic/GPS inversion do not compare favourably with the InSAR observations.

Tall buildings and flexible structures require a better characterization of long period ground motion spectra than the one provided by current seismic building codes. Motivated by that, a methodology is proposed and tested to improve recorded and synthetic ground motions which are consistent with the observed co-seismic displacement field obtained from interferometric synthetic aperture radar (InSAR) analysis of image data for the Tocopilla 2007 earthquake (Mw=7.7) in Northern Chile. A methodology is proposed to correct the observed motions such that, after double integration, they are coherent with the local value of the residual displacement. Synthetic records are generated by using a stochastic finite-fault model coupled with a long period pulse to capture the long period fling effect.It is observed that the proposed co-seismic correction yields records with more accurate long-period spectral components as compared with regular correction schemes such as acausal filtering. These signals provide an estimate for the velocity and displacement spectra, which are essential for tall-building design. Furthermore, hints are provided as to the shape of long-period spectra for seismic zones prone to large co-seismic displacements such as the Nazca-South American zone.

The high-frequency seismic field near the epicenter of a large earthquake is modeled by subdividing the fault plane into subelements and summing their contributions at the observation point. Each element is treated as a point source with an ω2 spectral shape, where ω is the angular frequency. Ground-motion contributions from the subsources are calculated using a stochastic model. Attenuation is based on simple geometric spreading in a whole space, coupled with regional anelastic attenuation (Q operator).
The form of the ωn spectrum with natural n follows from point shear-dislocation theory with an appropriately chosen slip time function. The seismic moment and corner frequency are the two parameters defining the point-source spectrum and must be linked to the subfault size to make the method complete. Two coefficients, Δσ and K, provide this link. Assigning a moment to a subfault of specified size introduces the stress parameter, Δσ. The relationship between corner frequency (dislocation growth rate) and fault size is established through the coefficient K, which is inherently nonunique. These two parameters control the number of subsources and the amplitudes of high-frequency radiation, respectively. Derivation of the model from shear-dislocation theory reveals the unavoidable uncertainty in assigning ωn spectrum to faults with finite size. This uncertainty can only be reduced through empirical validation.
The method is verified by simulating data recorded on rock sites near epicenters of the M8.0 1985 Michoacan (Mexico), the M8.0 1985 Valparaíso (Chile), and the M5.8 1988 Saguenay (Québec) earthquakes. Each of these events is among the largest for which strong-motion records are available, in their respective tectonic environments. The simulations for the first two earthquakes are compared to the more detailed modeling of Somerville et al. (1991), which employs an empirical source function and represents the effects of crustal structure using the theoretical impulse response. Both methods predict the observations accurately on average. The precision of the methods is also approximately equal; the predicted acceleration amplitudes in our model are generally within 15% of observations. An unexpected result of this study is that a single value of a parameter K provides a good fit to the data at high frequencies for all three earthquakes, despite their different tectonic environments. This suggests a simplicity in the modeling of source processes that was unanticipated.

Broadband (0.1-20 Hz) synthetic seismograms for finite-fault sources were produced for a model where stress drop is constant with seismic moment to see if they can match the magnitude dependence and distance decay of response spectral amplitudes found in the Next Generation Attenuation (NGA) relations recently developed from strong-motion data of crustal earthquakes in tectonically active regions. The broadband synthetics were constructed for earthquakes of M 5.5, 6.5, and 7.5 by combining deterministic synthetics for plane-layered models at low frequencies with stochastic synthetics at high frequencies. The stochastic portion used a source model where the Brune stress drop of 100 bars is constant with seismic moment. The deterministic synthetics were calculated using an average slip velocity, and hence, dynamic stress drop, on the fault that is uniform with magnitude. One novel aspect of this procedure is that the transition frequency between the deterministic and stochastic portions varied with magnitude, so that the transition frequency is inversely related to the rise time of slip on the fault. The spectral accelerations at 0.2, 1.0, and 3.0 sec periods from the synthetics generally agreed with those from the set of NGA relations for M 5.5-7.5 for distances of 2-100 km. At distances of 100-200 km some of the NGA relations for 0.2 sec spectral acceleration were substantially larger than the values of the synthetics for M 7.5 and M 6.5 earthquakes because these relations do not have a term accounting for Q. At 3 and 5 sec periods, the synthetics for M 7.5 earthquakes generally had larger spectral accelerations than the NGA relations, although there was large scatter in the results from the synthetics. The synthetics showed a sag in response spectra at close-in distances for M 5.5 between 0.3 and 0.7 sec that is not predicted from the NGA relations.

Practical procedures for modeling basin structure are proposed. One is to construct a smooth 3D basin structure model under
and around the target site for low-frequency strong motion simulation. The other is to make a 1D velocity structure model
just under the target site for high frequencies. These procedures were applied to the Osaka basin, Japan, in which numerous
exploration studies were conducted before and after the 1995 Hyogoken-Nanbu (Kobe) Earthquake. The published results of those
explorations in addition to those from our several investigations were compiled to construct the model.
A two-dimensional third-order B-spline function was used to establish a smooth structure model from available depth data.
Microtremor array observations were used to model the velocities and densities of the sedimentary layer structures. A four-layer
model well explains the dispersion characteristics of Rayleigh waves that make up the microtremors. By adding a detailed shallow
velocity structure to the top of the deeper four-layer model, adequate site responses for a wide frequency range of ground
motions can be obtained. This proposed procedure can be used to determine the basement geometry of other sedimentary basins.

We present a new approach for computing broadband (0–10 Hz) syn-thetic seismograms by combining high-frequency (HF) scattering with low-frequency (LF) deterministic seismograms, considering finite-fault earthquake rupture models embedded in 3D earth structure. Site-specific HF-scattering Green's functions for a heterogeneous medium with uniformly distributed random isotropic scatterers are convolved with a source-time function that characterizes the temporal evolution of the rupture process. These scatterograms are then reconciled with the LF-deterministic waveforms using a frequency-domain optimization to match both amplitude and phase spectra around the target intersection frequency. The scattering parameters of the medium, scattering attenuation η s , intrinsic attenuation η i , and site-kappa, as well as frequency-dependent attenuation, determine waveform and spectral character of the HF-synthetics and thus affect the hybrid broadband seismograms. Applying our meth-odology to the 1994 Northridge earthquake and validating against near-field record-ings at 24 sites, we find that our technique provides realistic broadband waveforms and consistently reproduces LF ground-motion intensities for two independent source descriptions. The least biased results, compared to recorded strong-motion data, are obtained after applying a frequency-dependent site-amplification factor to the broad-band simulations. This innovative hybrid ground-motion simulation approach, applic-able to any arbitrarily complex earthquake source model, is well suited for seismic hazard analysis and ground-motion estimation.

SummaryA simple and unified approach is presented to solve both the elasto-dynamic and elasto-static problems of point sources in a multi-layered half-space by using the Thompson-Haskell propagator matrix technique. It is shown that the apparent incompatibility between the two is associated with the degeneracy of the dynamic problem when ω= 0 and both can be handled uniformly using the Jordan canonical forms of matrices. We re-derive the propagator matrices for both the dynamic and static cases. We then show that the dynamic propagator matrix and the solution converge to their static counterparts as ω→ 0. Satisfactory static deformation can be obtained numerically using the dynamic solution at near-zero frequency.

We present a hybrid method for computing broadband strong motion seismograms in the near-field of large earthquakes. We combine complete seismograms at low-frequency with ray-theory seismograms at high-frequency to form a composite broadband seismogram that spans the entire frequency range of interest. In our approach, the amplitude spectra of the two sets of synthetic seismograms are reconciled at intermediate frequencies where their domain of validity overlaps.We demonstrate the method with scenario earthquakes based on the spatial random-field model for complex earthquake slip [J. Geophys. Res. 107 (B11) (2002) 2308]. The hybrid near-source, broadband seismograms are useful both for detailed source modeling and for incorporating source effects into probabilistic seismic hazard analysis.

The magnitude-8.8 Maule (Chile) earthquake of 27 February 2010 ruptured a segment of the Andean subduction zone megathrust that has been suspected to be of high seismic potential. It is the largest earthquake to rupture a mature seismic gap in a subduction zone that has been monitored with a dense space-geodetic network before the event. This provides an image of the pre-seismically locked state of the plate interface of unprecedentedly high resolution, allowing for an assessment of the spatial correlation of interseismic locking with coseismic slip. Pre-seismic locking might be used to anticipate future ruptures in many seismic gaps, given the fundamental assumption that locking and slip are similar. This hypothesis, however, could not be tested without the occurrence of the first gap-filling earthquake. Here we show evidence that the 2010 Maule earthquake slip distribution correlates closely with the patchwork of interseismic locking distribution as derived by inversion of global positioning system (GPS) observations during the previous decade. The earthquake nucleated in a region of high locking gradient and released most of the stresses accumulated in the area since the last major event in 1835. Two regions of high seismic slip (asperities) appeared to be nearly fully locked before the earthquake. Between these asperities, the rupture bridged a zone that was creeping interseismically with consistently low coseismic slip. The rupture stopped in areas that were highly locked before the earthquake but where pre-stress had been significantly reduced by overlapping twentieth-century earthquakes. Our work suggests that coseismic slip heterogeneity at the scale of single asperities should indicate the seismic potential of future great earthquakes, which thus might be anticipated by geodetic observations.

GAMMA SAR and interferomet-862 ric processing software

- C Werner
- U Wegmüller
- T Strozzi
- A Wiesmann

Werner, C., U. Wegmüller, T. Strozzi, and A. Wiesmann (2000). GAMMA SAR and interferomet-862
ric processing software, in ERS-ENVISAT Symposium, 16-20, Gothenburg, Sweden.